Stochastic Maximum Principle for Optimal Control Problems of Forward-Backward Delay Systems Involving Impulse Controls

WANG Shujun ,WU Zhen

1. School of Mathematics, Shandong University, Jinan 250100, China.
• Online:2017-04-25 Published:2017-03-24

WANG Shujun,WU Zhen. Stochastic Maximum Principle for Optimal Control Problems of Forward-Backward Delay Systems Involving Impulse Controls[J]. Journal of Systems Science and Complexity, 2017, 30(2): 280-306.

This paper is concerned with the optimal control problems of forward-backward delay systems involving impulse controls. The authors establish a stochastic maximum principle for this kind of systems. The most distinguishing features of the proposed problem are that the control variables consist of regular and impulsive controls, both with time delay, and that the domain of regular control is not necessarily convex. The authors obtain the necessary and sufficient conditions for optimal controls, which have potential applications in mathematical finance.

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